{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4G25BNOUSYF6RIQSAFBF4TFSSL","short_pith_number":"pith:4G25BNOU","schema_version":"1.0","canonical_sha256":"e1b5d0b5d4960be8a21201425e4cb292c5ff5f3908834e5959baa6a35056c042","source":{"kind":"arxiv","id":"1612.07011","version":1},"attestation_state":"computed","paper":{"title":"Structured backward error analysis of linearized structured polynomial eigenvalue problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Froil\\'an M. Dopico, Javier P\\'erez, Paul Van Dooren","submitted_at":"2016-12-21T08:33:55Z","abstract_excerpt":"We introduce a new class of structured matrix polynomials, namely, the class of M_A-structured matrix polynomials, to provide a common framework for many classes of structured matrix polynomials that are important in applications: the classes of (skew-)symmetric, (anti-)palindromic, and alternating matrix polynomials. Then, we introduce the families of M_A-structured strong block minimal bases pencils and of M_A-structured block Kronecker pencils,, and show that any M_A-structured odd-degree matrix polynomial can be strongly linearized via an M_A-structured block Kronecker pencil. Finally, for"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1612.07011","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-21T08:33:55Z","cross_cats_sorted":[],"title_canon_sha256":"0e7e0e3dbbd2fbfe2cf84dfe54e6b2bb96eb8b49f4b07f2a1c6fa276f0552702","abstract_canon_sha256":"e2cb7cff9bd27cb7cd8d9835e6c6fbf7d0f6ade1dfdf80db2a1ddb037078929e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:14.857871Z","signature_b64":"8B2mIH3xy+x2dcmUL8r+MTX4blBWxtslpTn4EOiKcwZ15i1Hcdff6936QLoX0VOsB/qX4y0i6V+M2LD5jt1rCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1b5d0b5d4960be8a21201425e4cb292c5ff5f3908834e5959baa6a35056c042","last_reissued_at":"2026-05-18T00:54:14.857209Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:14.857209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Structured backward error analysis of linearized structured polynomial eigenvalue problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Froil\\'an M. Dopico, Javier P\\'erez, Paul Van Dooren","submitted_at":"2016-12-21T08:33:55Z","abstract_excerpt":"We introduce a new class of structured matrix polynomials, namely, the class of M_A-structured matrix polynomials, to provide a common framework for many classes of structured matrix polynomials that are important in applications: the classes of (skew-)symmetric, (anti-)palindromic, and alternating matrix polynomials. Then, we introduce the families of M_A-structured strong block minimal bases pencils and of M_A-structured block Kronecker pencils,, and show that any M_A-structured odd-degree matrix polynomial can be strongly linearized via an M_A-structured block Kronecker pencil. Finally, for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07011","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1612.07011","created_at":"2026-05-18T00:54:14.857426+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.07011v1","created_at":"2026-05-18T00:54:14.857426+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07011","created_at":"2026-05-18T00:54:14.857426+00:00"},{"alias_kind":"pith_short_12","alias_value":"4G25BNOUSYF6","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4G25BNOUSYF6RIQS","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4G25BNOU","created_at":"2026-05-18T12:29:58.707656+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4G25BNOUSYF6RIQSAFBF4TFSSL","json":"https://pith.science/pith/4G25BNOUSYF6RIQSAFBF4TFSSL.json","graph_json":"https://pith.science/api/pith-number/4G25BNOUSYF6RIQSAFBF4TFSSL/graph.json","events_json":"https://pith.science/api/pith-number/4G25BNOUSYF6RIQSAFBF4TFSSL/events.json","paper":"https://pith.science/paper/4G25BNOU"},"agent_actions":{"view_html":"https://pith.science/pith/4G25BNOUSYF6RIQSAFBF4TFSSL","download_json":"https://pith.science/pith/4G25BNOUSYF6RIQSAFBF4TFSSL.json","view_paper":"https://pith.science/paper/4G25BNOU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.07011&json=true","fetch_graph":"https://pith.science/api/pith-number/4G25BNOUSYF6RIQSAFBF4TFSSL/graph.json","fetch_events":"https://pith.science/api/pith-number/4G25BNOUSYF6RIQSAFBF4TFSSL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4G25BNOUSYF6RIQSAFBF4TFSSL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4G25BNOUSYF6RIQSAFBF4TFSSL/action/storage_attestation","attest_author":"https://pith.science/pith/4G25BNOUSYF6RIQSAFBF4TFSSL/action/author_attestation","sign_citation":"https://pith.science/pith/4G25BNOUSYF6RIQSAFBF4TFSSL/action/citation_signature","submit_replication":"https://pith.science/pith/4G25BNOUSYF6RIQSAFBF4TFSSL/action/replication_record"}},"created_at":"2026-05-18T00:54:14.857426+00:00","updated_at":"2026-05-18T00:54:14.857426+00:00"}